Cross-set scale: Difference between revisions
Created page with "A '''cross-set scale''' is a scale generated by taking the Cartesian product of two or more scales, or of a scale with itself. As reported..." |
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A '''cross-set scale''' is a [[scale]] generated by taking the [[Wikipedia:Cartesian product|Cartesian product]] of two or more scales, or of a scale with itself. | A '''cross-set scale''' is a [[scale]] generated by taking every ordered pair in the [[Wikipedia:Cartesian product|Cartesian product]] of two or more scales, or of a scale with itself, and stacking all elements in each ordered pair: | ||
<math>\text{Cross-set}(A, B, ..., Z) = \{ a + b + \cdots + z : (a, b, ..., z) \in A \times B \times \cdots \times Z\}</math> | |||
In combinatorics, this operation is called a [[wikipedia:Sumset|sumset]]. | |||
As reported by [[Nick Vuci]], "the term Cross-Set as applied to scales is apparently the invention of Praveen Venkataramana". | As reported by [[Nick Vuci]], "the term Cross-Set as applied to scales is apparently the invention of Praveen Venkataramana". | ||